Editing Kernel (category theory) (section)

==Relationship to algebraic kernels==
[[Universal algebra]] defines a [[kernel (universal algebra)|notion of kernel]] for homomorphisms between two [[algebraic structure]]s of the same kind.
This concept of kernel measures how far the given homomorphism is from being [[injective]].
There is some overlap between this algebraic notion and the categorical notion of kernel since both generalize the situation of groups and modules mentioned above.
In general, however, the universal-algebraic notion of kernel is more like the category-theoretic concept of [[kernel pair]].
In particular, kernel pairs can be used to interpret kernels in monoid theory or ring theory in category-theoretic terms.